Automatic detection of floating mines by passive sensing is of major interest, yet remains a hard problem. In this paper, we propose an algorithm to detect them in infrared sequences, based on their geometry, provided by spatial derivatives. In infrared images, floating mines contrast with the sea due to the difference of emissivity at low incidence angles: they form bright elliptical areas. Using the available data and the geometry of our camera, we first determine the scales of interest, which represent the possible size of mines in number of pixels. Then, we use a temporal and a morphological filter to perform smoothing in the time dimension and contrast enhancement in the space dimensions, at the selected scales, and calculate for every pixel the Hessian matrix, composed of the second order derivatives, which are estimated in the classical scale-space framework, by convolving the image with derivatives of Gaussian. Based on the eigenvalues of the Hessian matrix, representing the curvatures along the principal directions of the image, we define two parameters describing the eccentricity of an elliptical area and the contrast with sea, and propose a measure of "mine-likeliness" that will be high for bright elliptical regions with selected eccentricy. At the end, we only retain pixels with high mine-likeliness, stable in time, as potential mines. Using a dataset of 10 sequences with ground truth, we evaluated the performance and stability of our algorithm, and obtained a precision between 80% and 100%, and a per-frame recall between 30% and 100%, depending on the difficulty of the scenarios.